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Copy pathSplitArrayLargestSum.java
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164 lines (150 loc) · 5.79 KB
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import java.util.Arrays;
public final class SplitArrayLargestSum {
private static int minimizeMaximum(int[] nums, int m) {
int max = 0;
int sum = 0;
for (int i : nums) {
max = Math.max(max, i);
sum += i;
}
int low = max;
int high = sum;
while (low < high) {
final int mid = low + (high - low) / 2;
final int pieces = cut(nums, mid);
if (pieces > m) {
low = mid + 1;
} else {
high = mid;
}
}
return low;
}
private static int maximizeMinimum(int[] chocolate, int m) {
int min = Integer.MAX_VALUE;
int sum = 0;
for (int i : chocolate) {
min = Math.min(min, i);
sum += i;
}
int low = min;
int high = sum;
while (low < high) {
final int mid = (low + high + 1) >>> 1;
if (split(chocolate, mid) < m) {
high = mid - 1;
} else {
low = mid;
}
}
return low;
}
private static int cut(int[] arr, int mid) {
int pieces = 1;
int largest = 0;
for (int i : arr) {
largest += i;
if (largest > mid) {
largest = i;
pieces++;
}
}
return pieces;
}
private static int split(int[] chocolate, int minSweetness) {
int peopleCount = 0;
int sweetness = 0;
for (int val : chocolate) {
sweetness += val;
if (sweetness >= minSweetness) {
peopleCount++;
sweetness = 0;
}
}
return peopleCount;
}
private static int maxMinR(int[] chocolate, int m) {
return findMaxMinOrMinMaxPartitionR(chocolate, m, true);
}
private static int maxMin(int[] chocolate, int m) {
return findMaxMinOrMinMaxPartition(chocolate, m, true);
}
private static int minMaxR(int[] chocolate, int m) {
return findMaxMinOrMinMaxPartitionR(chocolate, m, false);
}
private static int minMax(int[] chocolate, int m) {
return findMaxMinOrMinMaxPartition(chocolate, m, false);
}
// Top down DP
private static int findMaxMinOrMinMaxPartitionR(int[] nums, int m, boolean maxMin) {
final int[][] dp = new int[nums.length][m + 1];
final int[] sum = new int[nums.length];
for (int i = nums.length - 1; i >= 0; i--) {
sum[i] = (i == nums.length - 1 ? 0 : sum[i + 1]) + nums[i];
}
return recurse(nums, 0, m, sum, dp, maxMin);
}
private static int recurse(int[] nums, int start, int m, int[] sums, int[][] dp, boolean maxMin) {
if (m == 1) {
return sums[start];
}
if (dp[start][m] > 0) {
return dp[start][m];
}
int min = maxMin ? 0 : Integer.MAX_VALUE, sum = 0;
for (int i = start; i <= nums.length - m; i++) {
sum += nums[i];
min = maxMin ? Math.max(Math.min(sum, recurse(nums, i + 1, m - 1, sums, dp, true)), min)
: Math.min(Math.max(sum, recurse(nums, i + 1, m - 1, sums, dp, false)), min);
}
dp[start][m] = min;
return dp[start][m];
}
// Bottom up DP
private static int findMaxMinOrMinMaxPartition(int[] nums, int m, boolean maxMin) {
final int[] sums = new int[nums.length + 1];
final int[][] dp = new int[m + 1][nums.length + 1];
for (int i = 1; i <= nums.length; ++i) {
sums[i] = sums[i - 1] + nums[i - 1];
}
for (int[] row : dp) {
Arrays.fill(row, maxMin ? 0 : Integer.MAX_VALUE);
}
dp[0][0] = maxMin ? Integer.MAX_VALUE : 0;
for (int row = 1; row <= m; row++) {
for (int col = 1; col <= nums.length; col++) {
for (int k = row - 1; k < col; k++) {
dp[row][col] = maxMin
? Math.max(dp[row][col], Math.min(dp[row - 1][k], sums[col] - sums[k]))
: Math.min(dp[row][col], Math.max(dp[row - 1][k], sums[col] - sums[k]));
}
}
}
return dp[m][nums.length];
}
public static void main(String[] args) {
System.out.println(minimizeMaximum(new int[] { 7, 2, 5, 10, 8 }, 2));
System.out.println(minimizeMaximum(new int[] { 6, 3, 2, 8, 7, 5 }, 3));
System.out.println(minimizeMaximum(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 6));
System.out.println();
System.out.println(maximizeMinimum(new int[] { 7, 2, 5, 10, 8 }, 2));
System.out.println(maximizeMinimum(new int[] { 6, 3, 2, 8, 7, 5 }, 3));
System.out.println(maximizeMinimum(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 6));
System.out.println();
System.out.println(minMaxR(new int[] { 7, 2, 5, 10, 8 }, 2));
System.out.println(minMaxR(new int[] { 6, 3, 2, 8, 7, 5 }, 3));
System.out.println(minMaxR(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 6));
System.out.println();
System.out.println(maxMinR(new int[] { 7, 2, 5, 10, 8 }, 2));
System.out.println(maxMinR(new int[] { 6, 3, 2, 8, 7, 5 }, 3));
System.out.println(maxMinR(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 6));
System.out.println();
System.out.println(minMax(new int[] { 7, 2, 5, 10, 8 }, 2));
System.out.println(minMax(new int[] { 6, 3, 2, 8, 7, 5 }, 3));
System.out.println(minMax(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 6));
System.out.println();
System.out.println(maxMin(new int[] { 7, 2, 5, 10, 8 }, 2));
System.out.println(maxMin(new int[] { 6, 3, 2, 8, 7, 5 }, 3));
System.out.println(maxMin(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 6));
}
}